Optimal implicit exponentially-fitted Runge-Kutta methods

被引：38
作者：
Vanden Berghe, G
Ixaru, LG
Van Daele, M
机构：
[1] Univ Ghent, Vakgrp Toegepaste Wiskunde & Informat, B-9000 Ghent, Belgium
[2] Dept Theoret Phys, Inst Phys & Nucl Engn, R-76900 Bucharest, Romania
来源：
COMPUTER PHYSICS COMMUNICATIONS | 2001年 / 140卷 / 03期
关键词：
implicit Runge-Kutta methods; initial-value problems; oscillating solutions; exponential fitting; stiff equations;
D O I：
10.1016/S0010-4655(01)00279-X
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
Implicit Runge-Kutta methods for first-order ODEs are considered and the problem of how frequencies should be tuned in order to obtain the maximal benefit from the exponential fitted versions of such algorithms is examined. The key to the answer lies in the analysis of the behaviour of the error. A two-stage implicit Runge-Kutta method is particularly investigated. Formulae for optimal frequencies are produced; in that case the order of the method is increased by one unit. A numerical experiment illustrates the properties of the developed algorithms. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：346 / 357
页数：12
相关论文
共 50 条
  • [41] Exponentially Fitted Symplectic Runge-Kutta-Nystrom Methods
    Monovasilis, Th.
    Kalogiratou, Z.
    Simos, T. E.
    [J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 1395 - 1398
  • [42] Generating optimal Runge-Kutta methods
    Androulakis, GS
    Grapsa, TN
    Vrahatis, MN
    [J]. PROCEEDINGS OF THE SIXTH INTERNATIONAL COLLOQUIUM ON DIFFERENTIAL EQUATIONS, 1996, : 1 - 7
  • [43] Exponentially Fitted Symplectic Runge-Kutta-Nystrom methods
    Monovasilis, Th.
    Kalogiratou, Z.
    Simos, T. E.
    [J]. APPLIED MATHEMATICS & INFORMATION SCIENCES, 2013, 7 (01): : 81 - 85
  • [44] Exponentially-fitted Numerov methods
    Vanden Berghe, G.
    Van Daele, M.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 200 (01) : 140 - 153
  • [45] An energy-preserving exponentially-fitted continuous stage Runge–Kutta method for Hamiltonian systems
    Yuto Miyatake
    [J]. BIT Numerical Mathematics, 2014, 54 : 777 - 799
  • [46] A Family of Exponentially-fitted Runge–Kutta Methods with Exponential Order Up to Three for the Numerical Solution of the Schrödinger Equation
    Z. A. Anastassi
    T. E. Simos
    [J]. Journal of Mathematical Chemistry, 2007, 41 : 79 - 100
  • [47] Sixth-order symmetric and symplectic exponentially fitted modified Runge-Kutta methods of Gauss type
    Calvo, M.
    Franco, J. M.
    Montijano, J. I.
    Randez, L.
    [J]. COMPUTER PHYSICS COMMUNICATIONS, 2008, 178 (10) : 732 - 744
  • [48] An Efficient Scheme for the Implementation of Implicit Runge-Kutta Methods
    Skvortsov, L. M.
    [J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2008, 48 (11) : 2007 - 2017
  • [49] Implicit Runge-Kutta Methods with Explicit Internal Stages
    Skvortsov, L. M.
    [J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2018, 58 (03) : 307 - 321
  • [50] On the Starting Algorithms for Fully Implicit Runge-Kutta Methods
    S. González-Pinto
    J. I. Montijano
    S. Pérez-Rodríguez
    [J]. BIT Numerical Mathematics, 2000, 40 : 685 - 714
12345